Design and Control of a Voice Coil Actuated Robot Arm for Human-Robot Interaction
by
John M. McBean
B.S. Mechanical Engineering
Massachusetts Institute of Technology, 2001
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2004
@ 2004 Massachusetts Institute of Technology
All rights reserved
Signature of Author..........................
Department of Mechanical Engineering
May 7, 2004
C ertified by.....................................
.........................
Cynthia Breazeal
Assistant Professor of Media Arts and Sciences
Thef6Supervisor
Approved by...................................
Woodie Flowers
Pappalardo Professor o
Mecha
echanical Engineering
ing Faculty Reader
...............
A ccepted by ..........................................
Ain Sonin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTI")E.
OF TECHNOLOGY
BARKER
JUL 2 0 2004
LIBRARIES
Design and Control of a Voice Coil Actuated Robot Arm for Human-Robot Interaction
by
John M. McBean
Submitted to the Department of Mechanical Engineering
on May 7, 2004 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
The growing field of human-robot interaction (HRI) demands robots that move fluidly,
gracefully, compliantly and safely. This thesis describes recent work in the design and
evaluation of long-travel voice coil actuators (VCAs) for use in robots intended for
interacting with people. The basic advantages and shortcomings of electromagnetic
actuators are discussed and evaluated in the context of human-robot interaction, and are
compared to alternative actuation technologies. Voice coil actuators have been chosen
for their controllability, ease of implementation, geometry, compliance, biomimetic
actuation characteristics, safety, quietness, and high power density. Several VCAs were
designed, constructed, and tested, and a 4 Degree of Freedom (DOF) robotic arm was
built as a test platform for the actuators themselves, and the control systems used to drive
them. Several control systems were developed and implemented that, when used with the
actuators, enable smooth, fast, life-like motion.
Thesis Supervisor: Cynthia Breazeal
Title: Assistant Professor of Media Arts and Sciences
2
ACKNOWLEDGEMENTS
My thesis is dedicated to my family. Thanks for the support and inspiration.
Thanks for pushing me just hard enough. Thanks for the encouragement, and for the
selfless enthusiasm. I am a fortunate son. And a grateful one.
Cynthia, it has been a pleasure working with you. Thank you for giving me such a
perfect research opportunity, with the freedom to pursue a new idea, and the trust
that it had potential. My graduate career could not have been better. And
congratulations on your newest family member. I wish you all the best!
Woodie Flowers, the past several years would have been very different had we not
started arguing about catapults 3 years ago. I'm terribly lucky to have gotten in your
way by convincing you that I was a liability. Thanks for asking tough questions, and
giving credit to my answers. I have learned so much from you.
Fred Cote in the Edgerton Center Machine Shop. While I owe it to you,
it would be an insult to say thanks just for the machining education. I thank you for
making it fun, keeping me on my toes, entertaining me, and teaching
me about more important things than machining. It has been enlightening.
Thank you Leslie Regan for all of your help in pulling this together.
Thanks to all of my friends, the reasons why I've had so much trouble leaving this place.
3
This research is the work of the Robotic Life Group and the MIT Media Laboratory. The
work is funded by the Digital Life and Things That Think consortia.
4
OUTLINE
CHAPTER 1. Introduction ............................................................................................
1.1
Thesis Outline .................................................................................................
1.2
M otivation......................................................................................................
1.3
Thesis Scope ...................................................................................................
CHAPTER 2. Background.............................................................................................
2.1
Robotic Actuator History ...............................................................................
2.2
Voice Coil Actuator Technology and Prior W ork .........................................
2.2.2
Voice Coil Actuators for Human-Robot Interaction..............................
CHAPTER 3. Voice Coil actuator design .....................................................................
3.1
Detailed Description of VCA Design...............................................................
3.2
Specifications.................................................................................................
3.2.2
Cost........................................................................................................
3.2.3
Efficiency ...............................................................................................
CHAPTER 4. Arm Design ................................................................................................
4.1
M echanical Design .......................................................................................
4.2
Actuation and Feedback..................................................................................
4.3
Electrical and Control Hardware ...................................................................
CHAPTER 5. Kinem atics and Dynam ics......................................................................
5.1
Kinem atics .....................................................................................................
5.2
Dynam ics .......................................................................................................
5.2.1
Actuator Constants.................................................................................
5.2.2
Effective Actuator Attachm ent Radius .................................................
5.2.3
Inertial and Gravitational Effects...........................................................
5.2.4
Viscous Damping ....................................................................................
5.2.5
Electrical Dynam ic M odel......................................................................
CHAPTER 6. Control System Design..........................................................................
6.1
Overview ........................................................................................................
6.2
PID Control System ........................................................................................
6.3
PID Control with Gain Scheduling ...............................................................
6.3.2
Position-Dependant A ctuator Constants...............................................
6.3.3
Gravitational Effects ...............................................................................
6.3.4
Varying Radius At Which The VCA Acts on Arm Segment ................
6.4
Model-Based Control System with PD Feedback ....................
CHAPTER 7. Results .....................................................................................................
7.1
A ctuator results...............................................................................................
7.1.1
Perform ance..........................................................................................
7.1.2
Shortcom ings..........................................................................................
7.2
Arm Results ...................................................................................................
7.2.1
Interactivity ............................................................................................
7.2.2
Strength ...................................................................................................
7.3
Overall System Results (w ith controllers)........................................................
7.3.1
Results w ith PID controller....................................................................
10
11
12
16
17
17
21
22
24
24
28
30
31
32
32
34
35
38
38
39
40
42
43
43
43
44
44
44
46
48
48
49
49
52
52
52
55
55
55
55
56
56
5
7.3.2
Results with PID controller with Gain Scheduling................................
7.3.3
Results with Model-Based Feedforward controller with PD feedback .... 61
CHAPTER 8. Future Work and Conclusion.................................................................
8.1
Future W ork ...................................................................................................
8.2
C onclusion .....................................................................................................
59
66
66
67
6
LIST OF FIGURES
10
CHA PTER 1. Introduction ............................................................................................
13
Robotic Life Group's robot, Leonardo ..............................................
Figure 1.1
14
Figure 1.2
Leonardo w ith his fur........................................................................
Closeup view of Leo's gearmotor-driven upper arm......................... 15
Figure 1.3
17
CHA PTER 2. B ackground.............................................................................................
Figure 2.1
Basic voice coil consisting of magnetic assembly and moving coil..... 21
24
CHAPTER 3. Voice Coil actuator design .....................................................................
Figure 3.1
Early prototype of radial field, square cross-section voice coil...... 24
25
Solid model of radial voice coil........................................................
Figure 3.2
26
Figure 3.3
Solid model of axial voice coil. .........................................................
Sectional view of the moving-magnet, axial VCA used in the wrist.... 27
Figure 3.4
28
Figure 3.5
Bicep and forearm voice coil actuators.............................................
Solid model of parallel stacked voice coil actuator ........................... 30
Figure 3.6
Measured zero-velocity holding power for the voice coil actuators..... 31
Figure 3.7
32
CHAPTER 4. Arm Design............................................
Figure 4.1
Solid model of 4 degree of freedom direct-drive arm........................ 32
33
Photo of clevis bearing preload technique ........................................
Figure 4.2
Figure 4.3
Photo of elbow joint springs for gravity compensation.................... 34
35
Photo of motor drivers and control hardware ...................................
Figure 4.4
36
Figure 4.5
Photo of the arm .................................................................................
Figure 4.6
Photo of a person interacting with the arm........................................ 37
38
CHAPTER 5. Kinematics and Dynamics .....................................................................
38
Schematic of kinematic arm structure ..............................................
Figure 5.1
Figure 5.2
Plot of position dependancy of wrist actuator constant ..................... 40
Figure 5.3
Linearization of position dependancy of wrist actuator constant ......... 41
5.4
Schematic of position dependency of actuator attachment radius........ 42
Figure
44
CHAPTER 6. Control System Design..........................................................................
Figure 6.1
Block diagram of PID controller for 4DOF arm................................ 45
45
Block diagram of wrist PID controller...............................................
Figure 6.2
Figure 6.3
Block diagram of 4DOF PID control system with gain scheduling ..... 47
Block diagram of model-based controller with PD feedback............ 50
Figure 6.4
52
C HA PTER 7. R esults ...................................................................................................
Figure 7.1
Plot of forearm and bicep actuator force performance ...................... 53
Upper arm roll tracking performance with PID control (9 rads/sec)... 57
Figure 7.2
Figure 7.3
Forearm roll tracking performance with PID control (9 rads/sec)....... 57
Figure 7.4
Plot of elbow tracking performance with PID control (9 rads/sec)..... 58
Plot of wrist tracking performance with PID control (9 rads/sec)....... 58
Figure 7.5
Figure 7.6
Plot of upper arm roll tracking performance with PID controller with
59
gain scheduling (9 rads/sec)......................................................................................
Plot of forearm roll tracking performance with PID controller with gain
Figure 7.7
60
scheduling (9 rads/sec)...............................................................................................
Plot of elbow tracking performance with PID controller with gain
Figure 7.8
60
scheduling (9 rads/sec)...............................................................................................
7
Figure 7.9
Plot of wrist tracking performance with PID controller with gain
scheduling (9 rads/sec).............................................................................................
Wrist actuator tracking performance with PD control, 40 rads/sec......
Figure 7.10
Plot of wrist actuator tracking performance with feedforward and
Figure 7.11
feedback control, 40 rads/sec....................................................................................
Plot of wrist actuator step response with simple PD control.............
Figure 7.12
Plot of wrist step response with feedback and feedforward control.....
Figure 7.13
Plot of wrist actuator tracking performance with feedforward and
Figure 7.14
feedback control, 80 rads/sec....................................................................................
CHAPTER 8. Future Work and Conclusion.................................................................
Photo of sealed, self-contained electro-hydraulic actuator................
Figure 8.1
61
62
62
63
64
65
66
67
8
LIST OF TABLES
CHAPTER 1. Introduction .............................................................................................
Table 1.1 Actuator functional requirements and corresponding characteristics.......
CHAPTER 2. Background.............................................................................................
Table 2.1 Actuator synopsis..................................................................................
CHAPTER 3. Voice Coil actuator design ...................................................................
Table 3.1 Actuator Parameters...............................................................................
CHAPTER 4. Arm Design ................................................................................................
Table 4.1 Arm design parameters .............................................................................
CHAPTER 5. Kinematics and Dynamics ......................................................................
CHAPTER 6. Control System Design...........................................................................
Table 6.1 Arm and actuator design parameters relevant to wrist control system
d ev elop m en t..................................................................................................................
CHAPTER 7. Results ...................................................................................................
Table 7.1 Actuator performance results.................................................................
CHAPTER 8. Future W ork and Conclusion..................................................................
10
16
17
18
24
28
32
33
38
44
51
52
54
66
9
CHAPTER 1.
INTRODUCTION
The field of robotics is growing rapidly, and its demands are widespread. Robotic
systems are typically comprised of mechanical hardware, electrical hardware, sensors,
actuators, and computers. In a myriad of different applications, robots sense information
about their own state as well as their environment, process that information, and act
within their environment to accomplish a goal. The diverse environments in which
different types of robots operate impose widely varying requirements in terms of the
quality, speed, accuracy, robustness and type of sensing, actuation and processing
employed. Consequently, the selection of appropriate sensing, actuation, and processing
technology for a robot is generally environment and application dependent. This thesis
investigates the selection of an actuator technology that pertains specifically to robots
designed to operate in environments where their primary goals involve interaction with
people. In the ideal case of a robot as a collaborator with a person, there must be an
effective information exchange between the person and the robot, as well as the effective
execution of the task at hand (if the task consists of something more than the interaction
itself). To fulfill these expectations, it is important for a robot to be able to convey and
perceive visual, auditory and tactile information, as well as to interact with and affect its
environment. This thesis addresses the implications of these requirements on the design,
selection and control of robotic actuators.
Since robots find use in areas ranging from microscopic-scale precision assembly
to dinosaur-sized amusement park monsters, there are nearly as many metrics for
evaluating actuator technologies as there are applications for them. Some typical metrics
for comparing robotic actuators are: strength, response speed, accuracy, robustness to
environmental conditions, durability (number of cycles to failure), mass, size, ease of
implementation, cost, controllability, sound, stiffness, form factor, safety and scalability
[2]. Currently, the majority of robots in operation are used in industrial environments.
Spray painting, welding, and pick and place assembly are examples of typical robot
applications. As such, the consideration of the interaction between robots and humans (if
considered at all) is generally limited to safety and ease of control of the robot by the
operator. Further, the actuator selection parameters are very different from those
considered for human-friendly, collaborative robots.
The actuator criteria imposed by robots intended for meaningful and useful
interaction with humans differ significantly from those imposed by industrial robots. Our
primary concern for such robotic actuators is quality of motion. For a rich and effective
human-robot interaction, robots must move smoothly, fluidly, and quietly. The motion
must be fast enough to make the interaction or the task execution unencumbering and
practical, while maintaining a slow enough pace that the human can keep up. The motion
must be compliant enough that physical contact between the human and the robot is not
dangerous or uncomfortable. Further, it may be important that the human be able to
physically guide the robot (in teaching the robot a task or a motion, for example), in
which case the robot's motion must be controllable in such a way that it is aware of,
robust to, and sympathetic to the touch of a person. This calls for actuators with low
mechanical impedances and variable stiffnesses that are readily force-controlled. For
certain applications it may also be important that the motion be convincingly organic, as
the rigid, precise motion of an industrial robot may not be desirable in a robot intended as
10
an entertaining companion for a human. In the case of robots of human or mammalian
form, the geometry of the actuators may also play an important role in their selection. If
the physical appearance, as well as the quality of motion, is to be convincingly organic,
actuators must be designed with sizes and shapes that fit seamlessly into organic forms.
Comparisons of robot actuator technologies typically reveal the appealing high
power densities of electromagnetic actuators, and the high pressures of hydraulic,
piezoelectric, shape memory alloy (SMA), and certain electro-active polymer (EAP)
actuators [1]. The conventional metrics of comparison for these actuators tend not to
clearly identify which technologies are most suitable for high degree of freedom robots
intended for tactile interaction with people. Such comparisons also tend to be misleading
in that they may overlook some of the bulky infrastructure required for the
implementation of the actuators. Hydraulic actuators, for example, are particularly
attractive for their high pressures, low power holding forces, and relatively high speeds.
It should not be overlooked, however, that hydraulic actuators are conventionally messy,
high maintenance, very stiff, and require large amounts of material overhead for pumps,
fluid lines, valves, accumulators and the like. In the selection and development of an
appropriate actuation technology for interactive robots, we have considered conventional
metrics of comparison (pressure, power density, and controllability), while giving careful
attention to the actuator demands that are specific to the field of human-robot interaction
(HRI). In short, these demands include quality of motion, quality of tactile interaction,
safety, form factor, noise level, robustness to overloading, and ease of implementation
and control.
Electromagnetic voice coil actuators (VCAs) show great promise to fulfill many
of the aforementioned requirements. They have high power densities, silent operation,
smooth, backlash-free motion, variable stiffness, relatively low cost, favorable form
factor, and are easily controlled. This thesis covers the design, implementation, control,
and evaluation of VCAs as robotic actuators.
1.]
THESIS OUTLINE
We begin in chapter 1 by discussing the requirements imposed on robotic
actuators by different fields, and examining the actuator requirements imposed by our
specific project within the field of HRI. This serves as the motivation for this thesis. In
chapter 2, we discuss the background of robotic actuators, as a means of establishing
baselines for comparison across many actuator metrics. We then introduce the work
being done on voice coil actuators. We discuss the attributes of voice coil actuators, their
advantages and shortcomings (specifically in the context of tactile human-robot
interaction), and design parameters that affect their performance. We also describe prior
work in the field of VCA technology. In chapter 3, we discuss more specifically the
design and construction of our VCAs. We discuss the tradeoffs in VCA design among
size, form factor, quality of motion, mass, cost, and controllability. In chapter 4 we
describe the implementation of the actuators in a 4 DOF robotic arm to be used in the
development of a collaborative robot. In chapter 5, we describe the kinematic and
dynamic modeling of the actuators and the arm. Chapter 6 is a discussion of the control
system design. We discuss the necessity of an adequate control system to take full
advantage of the actuator characteristics, and describe the different methods employed.
11
In chapter 7 we present the results. We discuss actuator performance, implementation
issues, advantages and shortcomings of the mechanical design, compatibility of the
components, control system performance, and overall system performance. Finally, in
chapter 8, we discuss conclusions and future work. We describe the overall potential of
VCAs as viable robotic actuators, as well as potential avenues of research for solving
some of the fundamental problems with VCAs. We describe possible developments to
ease their implementation and configuration, making them more effective and attractive
as replacements for conventional actuators.
1.2 MoTIVATiON
The Robotic Life group at the MIT media lab works on developing robots that are
socially, intellectually, and physically capable of interacting and collaborating with
humans. Currently, the robot used for the implementation and evaluation of the research
is Leonardo, a 66 degree of freedom expressive robot that stands approximately 70
centimeters tall. As can be seen in figure 1.1, Leonardo has a mammalian form factor,
with a skeletal and muscular structure resembling that of a small child. He is a nonmobile robot, with the majority of his actuators located on his body. The larger actuators
are located in the box on which Leonardo stands, and drive the joints via cables or
linkages. All of Leonardo's actuators are brushed DC motors with gearboxes, using
potentiometers and magnetic encoders for position and velocity feedback.
12
Figure 1.1
Robotic Life Group's robot, Leonardo
13
Vigure 1.2
Leonardo with his fur
DC motors have high volumetric power densities and low output torques.[l] As a
result, DC motors may be significantly smaller than human muscles to achieve similar
power outputs for a given joint. However, these high power outputs are achieved at high
speeds and low forces, necessitating large transmission ratios to attain the torques
demanded by robotic applications. Unfortunately, the use of such transmissions usually
implies the introduction of backlash, noise, bulk, mass, excessive stiffness, torque ripple,
and susceptibility to breakage. The peak torques achievable in small scale robotic
applications (like Leo) are generally limited by the strength and robustness of the
materials used in the gear train, rather than the ability of the motor to transform electrical
power into mechanical power. Such is the case with Leonardo's actuators. Most of
Leonardo's actuators have gear trains (see figure 1.3) with high ratios so that his joints
are effectively infinitely stiff (non-backdriveable) as viewed from his workspace.
14
Figure 1.3
Closeup view of Leo's gearmotor-driven upper arm
The implication is that smooth, safe contact between Leo and his environment (people
and objects) is difficult at best. Fluid, jitter-free motions at human-scale velocities and
accelerations are unachievable. Sudden forces exerted on Leo by people or objects in his
environment result in damage to his joints or his actuators. Tactile interactions with Leo
are rigid, unforgiving, and slow.
There is an obvious need for an improvement in the actuators used in robots such
as Leo, if they are to convey and interpret information effectively and exhibit a life-like
presence. Table 1.1 presents the general functional requirements that we have chosen as
being the most important in the development of actuators for a collaborative HRI robot.
The table lists specific actuator characteristics that will be necessary to achieve the
functional requirements.
15
Table
1.1
ACTUATOR FUNCTIONAL REQUIREMENTS AND CORRESPONDING CHARACTERISTICS
Functional Requirement
High Quality of Motion
High Quality of Tactile
Interaction
Safety
Organic form factor
Quiet operation
Robustness to overloading
Easy to implement and
control
Actuator Characteristics
-low backlash
-low coulombic friction/stiction
-low mechanical impedance
-moderate accelerations attainable
-inherent damping
-variable stiffness
-force or impedance controlled
-adequate strength
-high permissible control system gains
-low inertia
-high compliance
-force or impedance sensing means
-moderate power and force density (to minimize actuator
size)
-bilateral, push/pull actuation (to eliminate necessity of
opposed pairs)
-linear, as opposed to rotary actuators (to mimic muscle)
-small or no mechanical transmissions (minimize bulk)
-few moving parts
-low or no transmission ratios (eliminate high speed
mechanical contact)
-few mechanical parts.
-backdriveable
-high compliance
-minimize need for complex gear trains to change the
actuation direction
-use readily available materials
-low hysteresis
1.3 THESIS SCOPE
Leo needs new actuators. The goal of this thesis was to research, design and
construct voice coil actuators that will serve as viable replacements for the conventional
actuators used in robots such as Leo. We have designed and built a 4 degree of freedom
arm as an evaluation platform for the new actuators, and as a potential model arm for the
next generation of Leonardo. We also developed and evaluated control systems that
exploit the actuators' favorable characteristics to improve robot performance in the areas
where Leo is deficient.
16
CHAPTER 2.
BACKGROUND
2.1 ROBOTiC ACTUATOR HiSTORY
In this section we give an overview of the state of the art of robot actuator
technology. A comprehensive comparison of actuator technologies was published by
Hollerbach, Hunter, and Ballantyne in 1992 [1] and is still very much relevant today.
The vast majority of actuators used in robotic systems to date employ one or more of the
technologies described in that paper. Many of these technologies have been proven to be
robust, cheap, and readily available. Under a paradigm where robots are expected to be
bulky, dangerous, rigid, precise, and serve strictly industrial applications, many of these
conventional technologies excel. A recent push for biologically-inspired robots that
interact directly with humans has spurred much research in artificial muscles. Many of
these younger, biomimetic materials-based actuation technologies are beginning to
provide competition for conventional technologies as robotic actuators [2], [3], [7].
First, we will define some terms that will be used in the discussion of the different
actuation technologies. Power density is the amount of mechanical power output an
actuator can produce, normalized by its mass or volume. Mass power density is
measured in Watts per kilogram; Volume power density is measured in Watts per cubic
meter. Peakpressure is the maximum force an actuator can produce, divided by the
cross-sectional area of the actuator. Pressuredensity is the peak pressure attainable by
the actuator, normalized by its mass or volume. Maximum strain is the maximum
percentage by which the actuator can change its length while producing a force.
Efficiency refers to the overall energy conversion efficiency - the mechanical output
power of the actuator divided by the power input to the actuator (electrical, chemical, or
thermal). Finally, work density is the amount of work generated over one full cycle of an
actuator, divided by the actuator mass.
The following table comprises a combination of our own work and research, as
well as that of Madden, Hollerbach, Hunter, and Ballantyne [1], [2]. Attempts to make
fair comparisons of actuator technologies can be misleading, as universal metrics for
evaluating performance are difficult to find, and often do not take into full account all of
the components of the actuators. For example, note that no units have been chosen for
the comparison of the speeds of the different types of actuators. This is because a
rigorous experiment has not been conducted where each of the actuators is subjected to a
comparable speed or frequency response test; hence the speeds of the actuators are
loosely characterized and described in the table. Other examples of the potentially
misleading nature of actuator comparisons are the apparent high pressure and power
densities of hydraulic and pneumatic actuators. Conventionally, this evaluation neglects
the mass of the material overhead (pumps, valves, fluid lines, etc). This is acceptable
only for very high DOF robots, where the mass and volume of the material overhead is in
fact small compared to the overall mass of the system). We have attempted to highlight,
where possible, such ambiguities in actuator comparison. Further, we have made attempts
to describe the actuator characteristics that are especially relevant to HRI robot design.
17
Table 2.1
Technology
Mammalian
Muscle
Electromagnetic
(VCAs)
Hydraulic
Pneumatic
ACTUATOR SYNOPSIS
Description
Moderate peak stress (0.35 MPa)
Moderate strain (20%)
Moderate power density (50W/Kg)
High (and variable) compliance
Flexible form factor
Produces smooth, fluid motion
Low material overhead
Low-moderate pressure density
Moderate speeds
Unilateral (Pull-only) actuation
Inefficient at zero-velocity (holding) forces.
Low peak stress (0.05-0.1 MPa)
Large strain (50%)
High power density (200 W/Kg)
Efficiency varies from high (-90%) at high speeds and short strokes
to low (~5%) at low speeds and high stroke lengths
Fast
High compliance
Form factor compatible with human-form design
Produce smooth, backlash-free, quiet motion
Low material overhead.
Few moving parts; robust to overloading
Bi-directional (push-pull) actuation
High force applications require mechanical transformers
High peak stress (20 MPa)
Large strain (50%)
High power density (600 W/Kg) (difficult to account for material
overhead mass, and extremely high instantaneous power delivery)
High stiffness
Very high material overhead (valves, lines, pump, accumulator,
filters, etc)
High maintenance
Bilateral actuation
Moderate-high speeds (although inefficient at high speeds)
Moderate peak stress (0.7 MPa)
Large strain (50%)
High power density (200 W/Kg) (difficult to account for material
overhead mass, and extremely high instantaneous power delivery)
High efficiency (-90%)
Fast, but with moderate settling times due to compressible gas and
18
Pneuamatic
(cont'd)
control difficulty.
Moderate compliance
High material overhead
Bilateral actuation
Often loud
Piezoelectric
High peak stress (35 MPa)
Low strain (1%)
Very low power density (0.1 W/Kg)
Very high speeds (high frequency, very short stroke actuators - less
practical for robotic applications)
Moderate material (and control) overhead
Must be driven with high voltages
Quiet
Bilateral actuation
"Inchworm" and "Waverotor"- type actuators have been developed
with larger strains and lower stresses
High peak stress (10 MPa)
Low strain (2%)
Very high power density (5 W/Kg)
High efficiency (~80%)
High speeds are possible
Usually unilateral actuation
High material overhead (bulky magnets or coils are required for
Magnetostrictive
activation)
NiTi ShapeMemory Alloy
(Thermal)
Dielectric
Elastomers
Relaxor or
Ferroelectric
Polymers
Very high peak stress (200 MPa)
Low strain (1-8%)
Very high power density (100kW/kg)
Very low efficiency (<5%)
Very difficult to control
Slow
Low voltage activation
Low cycle life
Unilateral actuation
Can have good form factor for mammal-form robots
Moderate-high stress (1-10 MPa peak)
Moderate-large strains (20%-380%)
Moderate efficiency (15%-90%)
Fast
Require high voltages
Unilateral actuation
High material overhead (Pre-stretching mechanisms required)
High stress (45 MPa)
Low strain (<7%)
High work density (<lMJ/m 3)
High stiffness
19
Relaxor or
Ferroelectric
Polymers
(cont'd)
Liquid Crystal
Polymers
Conducting
Polymers
Exhibits hysteresis
High driving voltages (>1kV)
Unilateral actuation
, Large material overhead (power supply, control electronics)
Low-moderate stress (0.01-0.45 MPa)
Moderate-high strains (2%-45%, depending on whether thermal or
field induced strain)
Moderate-high efficiency
Difficult to control (creep)
New material
High driving voltages
Slow
High stress (5-34 MPa)
Low strain (2%)
High stiffness
Low driving voltage (-2V)
High work density (IOOkJ/m 3)
Slow
Molecular
Actuators
Bilateral actuation
Low efficiency
Moderate-high stress (>1 MPa)
Moderate-large strain (20%)
High work density (IOOkJ/m 3)
Low driving voltage (-2V)
Slow
Unilateral actuation
New technology
Carbon
Nanotubes
High stress (>1OMPa)
Very small strain (0.2%)
Low driving voltage (-2V)
Inefficient
Unilateral actuation
Expensive
Ionic Polymer
Metal
Composites
(IPMC)
Ferromagnetic
Shape Memory
Alloys
Large strain
Low driving voltage (<1 OV)
Unilateral actuation
Low efficiency
High stress (<9 MPa)
Small strain (<10%)
Fast
High efficiency
Unilateral actuation
High material overhead (field magnets)
20
2.2 VoicE CoiL ACTUATOR TECHNOLOGY AND PRIOR WORK
Voice coil actuators have been around for decades. They have been used
primarily as the sources of force in audio loudspeakers, and as drive mechanisms for disk
drive read heads. As described in Section 2.1, they are characterized by high power
densities, high bandwidths, and relatively low pressures. A voice coil (see figure 2.1) is
an electromagnetic actuator that generally consists of one or more coils of wire placed in
a magnetic field, such that there is a force is produced when current flows in the coil.
The voice coils discussed in this thesis use permanent magnets as the magnetic field
source.
isic voice coil consisting of magnetic assembly and moving coil
The force produced by the actuator (the voice coils described in this thesis are
linear, rather than rotary actuators) is given by:
F = nrdiBSinO;
(1)
where n is the total number of coils of wire, d is the average diameter of the coil, i is the
current in the wire, B is the magnetic field strength, and ? is the angle between the
magnetic flux lines and the direction of the current. The part of the actuator that moves,
21
and to which the load is attached is generally called the rotor,and the stationary part (in
this case, the part which houses the coils) is called the stator.
Focus areas for improving the force outputs of VCAs are evident from (1).
Square wire has been used to increase coil winding density (increasing n for a given
volume). Attempts to increase the currents thermally permissible in the coils include
development of low resistance coil materials, use of active cooling techniques [1], and
the use of ferromagnetic fluid suspended in the air gap between the coil and the magnet.
Since heat adversely affects that magnetic field strength of permanent magnets
(especially NdFeB), the benefits of increased heat dissipation are twofold. Much work
has been done to increase the magnetic field strength across the air gap. Permanent
magnet materials, such as NdFeB, with higher magnetic remanences and higher
temperature tolerances have been developed. Actuator geometries have been refined so
as to "focus" the flux in the air gap and minimize leakage [5]. The use of ferromagnetic
fluid also increases the field strength and uniformity, but its effects are limited due to its
low magnetic saturation. The preceding techniques have been shown to greatly improve
VCA performance. In the construction of these prototype actuators, however, we have
opted for a simple design, leaving room for the implementation of such techniques in
future revisions.
Voice coils are typically not commutated, meaning the entire coil becomes
energized when a voltage is applied. This represents a source of inefficiency for voice
coils, as waste heat is produced even in the coils that are not contributing significantly to
the force produced by the actuator. For this reason, VCAs with arbitrarily long strains are
not practical.
2.2.2
VoICE COIL ACTUATORS FOR HUMAN-ROBOTINTERACTION
For their application to HRI and force-controlled robots, VCAs have many
advantages over other forms of actuation [5],[6], [10]. The major advantages of
electromagnetic actuators are their speed, smooth motion, silent operation, high
efficiencies, ease of implementation, and robustness to overloading. If, for example, a
directly-driven VCA is pushed against the direction of its force, it will simply continue to
apply a force proportional to its current, and allow itself to be backdriven if the force
exceeds that value. Power input to the actuator in the form of current is then dissipated as
heat. This fundamental property of VCAs (and all backdriveable actuators) is a key
safety advantage for robots intended to touch, and be touched by, people. VCAs tend to
have only one moving part, with only two points of contact (bearings at either end). This
makes for an actuator with low wear, long life, quiet operation, and excellent shock
loading tolerance.
Another major advantage that VCAs have over mammalian muscle, and other
forms of actuation that imitate it closely, is that VCAs are bilateral actuators, meaning
they can push or pull with comparable force. This eliminates the cumbersome, bulky,
and often difficult to control need for bilaterally opposed pairs of actuators at every joint.
Effectively, the power density of VCAs ought to be compared to ha/f that of unilateral
actuators, when they are being considered as sources of force for robotic joints which will
undergo flexion and extension. If we consider the metric of Pressuredensity, bilateral
22
actuators (such as VCAs) have a twofold advantage over their unilateral counterparts
(such as muscle).
For high force applications, mechanical transformers (gear reductions, for
example) are needed to transform the power delivered by electromagnetic actuators from
high speed/low force to high force/low speed. Mechanical transformers usually introduce
backlash, noise, stiffness, and control problems. They also decrease robustness and
increase maintenance requirements. This, of course, is the fundamental problem with
VCAs, and necessitates that direct-drive robots using VCAs use larger actuators than
might be necessary if a different actuation technology were chosen, or if mechanical
transmissions were used. Due to their high power densities, electromagnetic actuators
sized to achieve a certain force for an application will be found to have higher power
outputs than required for the application. This mismatching of peak power and peak
pressure (where mechanical transformers, or geartrains are not used), is discussed further
in chapter 8. Our VCAs have demonstrated sufficient pressures to be free of the need for
mechanical transformers of any kind, for use in non-mobile, low-payload HRI robots
comparable in size, shape and strength to humans.
While rotary electromagnetic actuators (brushed or brushless DC motors, for
example) have similar performance characteristics to VCAs, they have a distinct
geometric disadvantage when compared to VCAs, for use in human-form robots. VCAs
have a similar form factor to human muscle - they can have large length/diameter ratios
(meshing symbiotically with limbs of mammalian-form robots); they can have
comparatively high strains; they are linear actuators, and can therefore be implemented in
ways that look and behave like mammalian muscles without the use of bulky, heavy, or
complex drivetrains. Rotary actuators, on the other hand, would have to be oriented
parallel (preferably concentric) with the axis of the joint, and in order to occupy the same
volume as a corresponding VCA, would have to have a diameter or length that would
extend far beyond the envelope of the form factor of a human limb. Further, if the rotary
actuator should be oriented in a more geometrically favorable way, a drivetrain may be
necessary to transmit the mechanical power from the actuator to the joint axis. Such
drivetrains introduce backlash, noise, jitter, stiffness, and control problems, while
increasing system mass, volume, and susceptibility to breakage.
The low peak pressures produced by VCAs (approx. a factor of 4 lower than that
of human muscle, for short durations) require that the actuators be oversized in
comparison to muscle, and are weaker than a muscle of similar size. Consequently, the
arm that is the subject of this thesis is approximately the size of that of a young child, and
has strength performance that ranges from significantly weaker than a child (for short
durations) to comparable strength to a child (for longer durations) [8]. Since many HRI
robots may find their applications in areas that do not require high payloads, high contact
forces, or high inertial forces, the compromise between decreased strength and smooth,
quiet, backlash-free, fast, easily-controlled motion seems acceptable.
23
CHAPTER 3.
VOICE COIL ACTUATOR DESIGN
3.1 DETAiLED DESCRiPTiON OF VCA DESIGN
We have experimented a variety of VCA designs. Figure 3.1 shows a moving coil design with a square cross section.
Figure 3.1
Early prototype of radial field, square cross-section voice coil
The stator, consisting of NdFeB permanent magnets is constructed such that there is a
uniform magnetic flux oriented from the inside (axis) of the actuator to the outside. It is a
2-dimensional approximation of a radial magnetic field. This design has the feature that
strains of significantly greater than 50% can be achieved, but at correspondingly lower
pressures than other designs would afford. Figure 3.2 shows a sectional view of a
possible embodiment of a radially magnetized voice coil design. The white arrows
represent the magnetic flux lines.
24
Radially Magnetized Tube
with Iron Core
High Permeability shell
Coil
Air Gap
Figure 3.2
Solid model of radial voice coil.
A radially magnetized tube with an iron core, concentric with an iron shell establishes a
magnetic field across the air gap. A major advantage to radial designs is the uniformity
of the field strength achievable along the length of the actuator. The cost, however, is
that it is difficult to radially magnetize permanent magnet materials, making them
expensive, and causing their field strengths to be typically 10-20% lower than axially
magnetized magnets of the same material. Figure 3.3 shows an axially magnetized
design, where, similarly to the radial design, the magnetic flux runs along the axis of the
magnetic core, into the iron shell at one end of the actuator, and then back across the
airgap to the core, to complete the magnetic circuit. The white arrows represent the
magnetic flux lines.
25
Coil
High Permeobility shell
dAolli Mognetized Cylinder
Figure 3.3
Solid model of axial voice coil.
The major difference between axial and radial designs is the uniformity of the flux in the
air gap, along the length of the actuator. While radial designs achieve relatively uniform
field strengths, axial designs tend to concentrate the flux near the open end of the air gap.
Just as an axially magnetized permanent magnet behaves in air, the radial component of
the flux is concentrated at the ends, not along the length, of the magnet. The axially
magnetized, moving coil VCA in figure 3.3 is a typical design and is commercially
available.
We have chosen a moving-magnet design, as opposed to moving coil design for
the VCAs to be used in the arm. While a moving-magnet design can result in a slightly
greater moving mass (this, of course, is not always the case and depends on the coil mass
and whether the VCA is being designed for high force or high speed operation), it affords
a simpler construction geometry enabling smaller, more streamlined actuators. A
sectional view of the wrist actuator can be seen in figure 3.4.
26
Potor shaft t Rvels linecriv)
S hof t support bearing
Ihin walled shell,
around which the coils
are wound
ton shell
-Coil I
AExiAy magnelized
rn
oving magne t fotor
.
Cod sp=cei
Shof t st.1ppott brarton
Acfuaoo support~
Figure 3.4
Sectional view of the moving-magnet, axial VCA used in the wrist
The stator consists of two independently wound coils inside a thin iron shell. The rotor is
a cylindrical, axially magnetized NdFeB permanent magnet, with shafts extending from
each pole, supported at the ends in linear bearings. The lengths of the rotor and the coils
are designed such that throughout the range of motion of the actuator, one coil remains in
the magnetic field of the south pole of the rotor; the other coil, the north. The current in
each of the two coils is in opposite directions, matching the opposing polarities of the
magnetic fields at either end of the rotor. The strokes of the bicep and wrist actuators are
4.7 cm and 2.5 cm, respectively. Figure 3.5 shows the finished bicep and forearm
actuators.
27
Figure 3.5
Bicep and forearm voice coil actuators
3.2 SPECIFCATONS
End effector forces of 20 N were desired on the arm, which correspond to peak
actuator forces of approximately 100 N and 50 N for the bicep and forearm actuators,
respectively. Table 3.1 shows the parameters for each actuator design, based on
assumptions of an average air gap field strength of 0.25 T, and magnetic field
perpendicular to the actuator coils.
Table 3.1
Desired
Peak Force
Peak
Current (I)
(F)
Forearm
Bicp
50N
100N
ACTUATOR PARAMETERS
Average
Field
Average Coil
Diameter (d)
Strength (B)
3A
3A
0.25T
0.25T
Number
of Coils
(n)
0.0287m
0.0405m
840
1352
28
The permanent magnets used in both the forearm and bicep VCAs are axially magnetized
NdFeB (grade N40) rods with surface field strengths of approximately 1.25 T. The most
significant unknown in the above table is the average air gap field strength. The flux
behavior across the air gap is difficult to measure or model. Consequently, empirical data
was collected (tests were done on a BEI voice coil), and conservative estimates were
made for the expected average field strength. Given the large degree of uncertainty in
this and other estimates, the table above incorporates a safety factor of 2 in terms of peak
actuator force.
We have built and tested a variation on this voice coil design (see figure. 3.6). By
effectively stacking smaller VCAs within one, and connecting their outputs to a common
rotor such that their forces sum in parallel, the limit on peak actuator pressure effectively
vanishes. Practical design considerations would of course limit the pressures achievable,
but the force produced in the actuator will grow linearly with length, while the diameter
stays constant. This of course would make VCAs look more attractive with respect to the
metric of peak pressure, once again making it difficult to characterize the actuators in a
normalized way such that they can be compared fairly with other technologies. The
technique of increasing length for higher force is relevant because it is often the case in
designing human-form robots (with limbs having high length/diameter ratios) that adding
width, or thickness to the actuators (limbs) is very costly, but longer actuators, as means
to higher forces, can be accommodated. A 3-stage prototype of a VCA using this design
has been built and has verified the possibility of increasing peak pressure in this manner,
but was not used in the construction of the direct-drive arm presented in this thesis.
29
~Mcqgr&
--xidly nicrelize~d
Figure 3.6
3.2.2
Solid model of parallel stacked voice coil actuator
COST
The VCAs constructed for this thesis use readily available materials. The internal
components (the coil separators, the shell around which the coils are wound, the
endplates) are machined from aluminum; the shafts are standard hardened steel shafts,
running in ceramic linear bearings. The outer shell is thin-walled steel tubing. The
assembly of the VCAs is entirely by press fit. As a result, with the exception of some
tight tolerance machining operations, the construction and assembly of VCAs is easy,
cheap and fast. Because VCAs have fewer moving parts, and do not involve delicate
mechanical components such as brushes and commutators, their cost, complexity and
manufacture times are lower than those of DC motors. As a result of the simplicity of
their design, they are also more robust to operating conditions than DC motors.
30
3.2.3
EFFICiENCY
A major shortcoming of VCAs is their inefficiency at low speeds. Their low
backdriveability necessitates that they consume significant amounts of power, even while
not moving. This problem can be alleviated to some extent by using springs and
carefully choosing the geometry of a robot so as to minimize constant loads, such as
gravitational forces. Robot design with voice coil actuators should therefore take
inspiration from the way human bodies are designed. Relaxed states should involve low
torques by ensuring that joints settle in local equilibria (stable equilibria, in the case of a
relaxed shoulder or elbow, or unstable equilibria as in the case of a locked knee in a lowenergy standing position). Figure 3.7 shows the measured zero-velocity power
consumption by the forearm and bicep actuators, as functions of holding torque.
Actuator Holding Power vs. Force
400
350
300
250
-
a. 200
Forearm Holding Power
- Bicep Holding Power
150
100
50
0
0
20
40
60
80
100
Force (N)
Figure 3.7
Measured zero-velocity holding power for the voice coil actuators
For small, non-mobile robots with low payload capacities, and whose main goals are
smooth, friendly interactions with humans, the tradeoff between efficiency and quality of
motion is acceptable.
31
CHAPTER 4.
ARM DESIGN
4.1 MECHANICAL DESiGN
Forc e/Torque sersor
e,A,
pper
cm
arc, bet
ienijr
DCO
-bceg
Lcower aum be--Ji,,
VCA
rcil DOF--
Figure 4.1
Solid model of 4 degree of freedom direct-drive arm
Figure 4.1 is a solid model of the 4DOF direct-drive robotic arm we have built.
VCAs drive the bicep and forearm degrees of freedom, while brushed DC motors are
driving the upper and lower arm roll degrees of freedom. The roll degrees of freedom are
necessary to give the arm enough dexterity to execute meaningful trajectories. The
geometry of the arm is modeled after a human, with a forearm slightly longer than the
upper arm. The end effector is currently a small knob. This is useful for developing and
evaluating the VCA mechanical and control systems, but in the future, hands with tactile
feedback may be implemented. The range of motion of the arm is comparable to that of a
32
human. The elbow and wrist have approximate ranges of motion (ROM) of 90', while
each of the roll degrees of freedom has an ROM of approximately 2000. Table 4.1
summarizes the properties of the arm.
Table 4.1
Peak End Effector Forces
Peak Acceleration (hand)
Peak Acceleration (forearm)
Joint Ranges of
Upper arm roll
Motion
Lower arm roll
Bicep
Dimensions
(lengths)
ARM DESIGN PARAMETERS
20N
2g
ig
2000
2000
90*
Wrist
900
Upper arm
Forearm
0.20m
0.1 7m
Hand
0.08m
The arm is constructed mainly of aluminum. The arm segments (or bone
structure) are sections of thin-walled aluminum tubing, to maximize stiffness and
minimize weight. All rotational axes use preloaded ball bearings, to ensure that the
structure of the arm does not compromise the smooth, muscle-like performance of the
actuators. The bearings minimize noise, backlash, and friction. Figure 4.2 shows the
method of using a set screw to spread the arms of the actuator clevis to apply an
adjustable preload to the clevis bearings.
Figure 4.2
Photo of clevis bearing preload technique
33
The upper arm roll and elbow degrees of freedom have preload springs to help
offset the gravitational torques due to the mass of the lower arm segments. The springs
are not necessary, but they improve the arm's performance, give it a more natural resting
position, and minimize the risk of sudden collisions when the power to the arm is turned
off. The elbow springs are shown in figure 4.3.
Figure 4.3
Photo of elbow joint springs
4.2 ACTUA TION AND FEEDBACK
The bicep and wrist degrees of freedom are driven by VCAs, and the angular
positions of the two joints are obtained via Hall Effect rotary position sensors (Honeywell
HRS 100). The VCAs attach to the arm segments upon which they act (forearm and
hand) at a distance from the joint that is approximately 115 th the length of that segment.
End effector forces are therefore approximately 115 th of actuator forces. The upper and
lower arm roll degrees of freedom are driven by Maxon Motors brushed DC motors. The
motors act on the roll segments of each arm via a 8:1 belt reduction. The reduction
allows for a moderate increase in torque, while maintaining a very high degree of
backdriveability, and minimizing problems associated with gearboxes. The belts
introduce no backlash, and they have some inherent damping that helps in the control of
the joint positions. Joint position and velocity information for the two roll degrees of
freedom are obtained via Maxon MR encoders on the backs of the roll motors.
34
For future control system development on the arm, there is a 6 axis force/torque
sensor in series with the upper arm, that will be used to measure inertial forces, as well as
gravitational forces (for future implementation of trajectory, force, impedance, or hybrid
control schemes). Local force sensors (closer to the end-effector) could be used to form
force-control loops around contact and payload forces. A potential future development
for VCAs is to include integrated position, velocity, and force sensors in the actuators
themselves.
4.3 ELECTRICAL AND CONTROL HARDWARE
The control system development for the arm was done on an IBM workstation,
using the DSP-based DSPACE prototyping hardware and software. The DSPACE
software interfaces with Matlab's Simulink program, and the hardware interfaces with the
sensors and actuators via a 8 channel ADC and a 8 channel DAC. All control system
software was developed and implemented using Matlab and Simulink. The amplifiers
used to drive the roll motors and the wrist VCA (the less powerful of the two VCAs) are
Maxon Motors linear amplifiers with peak current outputs of 2 Amps. The elbow VCA is
driven by a higher power Maxon Motors pulse width modulation-based controller with a
peak current output of 10 Amps. The opposing pairs of coils in each VCA are driven by
the same control signal, in opposite directions. Figure 4.4 shows the motor driver setup,
consisting of linear amplifiers, digital amplifier, and Dspace I/O board, used to drive the
arm.
Figure 4.4
Photo of motor drivers and control hardware
35
Finally, a photograph of the finished arm can be seen in figure 4.5.
Figure 4.-
Photo o1 the arm
36
37
CHAPTER 5.
KINEMATICS AND DYNAMICS
5.1 KINEMA TiCS
Figure 5.1 is a schematic of the 4 DOF arm. The 4 angles that describe the state
of the arm are denoted by 6h, 0 e, Of, and 0,. O6 and Of are the upper and lower roll angles,
respectively. Their axes are aligned with the axes of their respective arm segments.
Angles Oe and Ow are the angles of the VCA-actuated degrees of freedom, the elbow and
the wrist.
Ob (upper arm roll)
Ge (elbow angle)
ef (forearm arm roll)
Figure 5.1
w (wrist angle)
Schematic of kinematic arm structure
In the interest of conserving control bandwidth, all trajectory control tests were executed
in joint space, eliminating the need for real time computation of large jacobian matrices.
Conventional techniques for computing the inverse kinematics of a 4 DOF arm exist, but
were not necessary to effectively evaluate the performance of the VCAs, the arm, and the
controls systems developed.
38
With regard to the implementation of workspace-coordinate control systems
(based on the end effector positions, solved using forward and inverse kinematics), it is
important to note that the 4DOF arm is underconstrained with respect to the position of
the end effector alone, necessitating a sophisticated control algorithm that introduces
constraints between the different degrees of freedom, or imposes constraints on the
orientation (in addition to the position) of the end effector. For example, such a
constraint may attempt to keep the bicep joint angle as close to zero as possible, since it is
the most costly to move in terms of power consumption.
5.2 DYNAMiCS
The goal of implementing a model-based controller is to use knowledge of the
system parameters to give the controller feedforward information that will enable better
tracking performance for pre-scripted trajectories. Contrary to a gain scheduled
controller, a full dynamic model provides a priori estimates of control inputs that account
for position-dependant system parameters, desired state variables (and their time
derivatives), and prescribed trajectories (and their time derivatives). For the development
of such a model-based controller, simple PID controllers were used on the 2 roll degrees
of freedom and the elbow, maintaining constant (zero) angles at those joints. This
effectively reduces the 4DOF arm to a 1 DOF planar arm, for the purpose of focusing very
closely on the model and performance evaluation of the VCAs themselves. A full
dynamic model was created for the 1 DOF arm. The dynamic model takes into account
inertial forces, viscous damping, gravitational forces, actuator winding resistance and
inductance, position-dependant actuator attachment radius, and a position dependant
actuator constant, accounting for the non-linearities within the VCA. The dynamic model
for the VCA driving a IDOF arm is:
ii = [I/(Kmi Ri)]*[Ii6i+MigljCos6g + KbI];
(2)
Where Kmi is the position-dependant VCA actuator constant, Ri is the position-dependant
actuator attachment radius, Ii is the arm moment of inertia, O, is the angular acceleration
of the joint, M is the mass of the arm, 1,i is the distance to the centroid of the arm, ,giis
the gravitational angle of the joint (measured from horizontal), Ki is the viscous damping
constant for the joint, 6, is the angular velocity of the joint, and ii is the current input to
the VCA, which obeys the following first-order dynamics:
V,=Liji+Reii;
(3)
Where V is the control input (voltage) to the actuator, and Li and Rei are the coil
inductance and resistance, respectively. The following sections explain each of the terms
in the above dynamic equations.
39
5.2.1
ACTUATOR CONSTANTS
Ki is the VCA motor constant. Its units are N/Amp. Since the permanent magnet rotor
travels within the coils, the interaction between the induced and permanent magnetic
fields varies in strength, creating a position-dependant actuator constant. Effectively, the
actuator constant can be regarded as:
(4)
K,,i
= le1 * B
From (1), where 1c, and Bi are coil length and position-dependent magnetic field,
respectively. This non-linearity has been measured for each actuator, and the profile of
the position-dependent actuator constant, which is characteristic of both the bicep and
wrist actuators, is shown in figure (5.2).
Wrist VCA Force vs. Position
8
7
6
z
0
U.
4
Wrist VCA Force
i
2 i
1 0
0
0.005
0.01
0.015
0.02
0.025
0.03
Wrist VCA Position (m)
Figure 5.2
Plot of position dependancy of wrist actuator constant
40
For simplification, the relationship between actuator constant and joint angular position
has been linearized as follows:
For
O, ;Oimd :
K,=
[(Kia
Km
i min/ Oimid] Oi +Kmin ;
= [-(Kimax
-Kimin)/ Oid]*Oi +(Kimin
(5)
For 0. > 0.d:
K,
+2(Kimax-
Kimin));
(6)
Where Kimax and Kimin are the maximum and minimum actuator constants, ?hnid is the
middle of the range of motion of joint i, and ?i is the angle of joint i. For these
calculations, Kimax, Kimi and ?hnid were measured empirically, for the best accuracy.
This linearization describes an actuator profile as follows:
Linearized Wrist Actuator Constant vs. Position
8
--------------------------------
7
'V
6
0
5 i
(U
0
U
4
(U
3
U)
-+-
Linearized Wrist Actuator
Constant
2
1
0
I
IIIIi
0
0.005
0.01
0.015
0.02
0.025
0.03
Wrist VCA position (m)
Figure 5.3
Linearization of position dependancy of wrist actuator constant
41
5.2.2
EFFECTIVE ACTUATOR ATTACHMENT RADIUS
Ri is the distance from the point of attachment of the actuator clevis to the axis of rotation
of joint i, measured perpendicular to the axis of actuator i. It is the distance R, in figure
5.4.
Figure 5.4
Schematic of position dependency of actuator attachment radius
Ri is clearly position-dependant, and it varies according to:
R i = lai Cos(-r2
-,
-
,) ;2
(7)
Where each of the parameters lai, 6;, and 8 ai is defined in figure 5.4. For the calculation
of Ri, the axis of the actuator is assumed to be parallel to the arm segment to which it is
attached. In reality, this angle varies by less than 5'.
42
5.2.3
INERTIAL AND GRAVITATIONAL EFFECTS
The first 2 terms in equation (2) represent the torques due to the inertia of the arm,
and gravity. These are the dominant effects in the in the dynamic model for the arm. The
gravitational term helps to minimize steady state position error, and the inertial term
significantly improves tracking performance by adjusting the control signal based on
desired acceleration in place of desired position alone.
5.2.4
VIsCousDAMPING
The model includes a small amount of viscous damping. The primary source for
velocity-dependant damping is eddy current damping within the actuators, although small
amounts of viscous damping are present due to friction in the rotary encoders, and the
viscosity of the oil used on the actuator shafts.
5.2.5
ELECTRICAL DYNAMIC MODEL
A simple first-order model was used to represent the actuator coil electrical
dynamics. Equation (3) shows this model, where Li and Rei are the measured coil
inductance and resistance of the respective actuators. Given the large size of the
actuators, and the small size of the arm segment, the electrical time constant of the
actuator coils is significant, necessitating these terms in the dynamic model.
The resultant system model is third order, with voltages to the actuators as the
control inputs, and angular positions of the joints (and their first and second derivatives)
as state variables.
43
CHAPTER 6.
CONTROL SYSTEM DESIGN
6.1 OVERVIEW
Three control systems were implemented on the arm, in attempts to explore the
potential of VCAs as robotic actuators, and to exploit their best characteristics. The first
control system developed is a basic PID controller with full state feedback. The PID
controller was implemented on all 4 degrees of freedom, and basic trajectory tracking
tasks were executed in joint space. The second control system developed is a PID
controller with gain scheduling that varies the control gains to account for some of the
dominant non-linearities in the actuators themselves, as well as in the construction of the
arm. The gain-scheduled PID controller was implemented on all 4 degrees of freedom,
and once again trajectory tracking tasks were executed in joint space. Third, a more
sophisticated model-based controller was implemented on an individual VCA-driven
joint, with dynamic model-based feedforward compensation in addition to PD feedback.
A full dynamic model was created for one of the VCAs (the wrist actuator), in an attempt
to characterize it well enough to improve controller performance. As a means of
exclusively testing the dynamic model of the VCA itself, the model-based controller was
only implemented on one degree of freedom, however, it can be extended to multiple
degrees of freedom using conventional techniques [6].
6.2 PID CONTROL SYSTEM
The first control system implemented on the arm was a simple PID controller,
implemented on all 4 degrees of freedom. No system model was used, and all nonlinearities were ignored. Feedback gains were determined empirically, since parameters
that were difficult to characterize determine the stability of the system.
The block diagram of the PID control system for the 4DOF arm is shown in figure 6.1.
44
4 DEGREE OF FREEDOM PID CONTROLLER
OUTPUT SIGNALS TO DC (ROLL) MOTOR CONTROLLERS
ENCODERP OSITIONNELOCITY SENSOR SIGNALS
E
:t:-forearm
DAC
roll positon
Eno delta positionA
DS1 104ENCPOSCl
Ini
In2
-1
C
0Oft
C2
roll
control signal
forearm roll velocity
00t2 upper aim
0 upper aim roll position
I
DS1104ENCP
forearm
E14DCC
upper arm roil
roll control signal
DSIIO4DAC_2
Upper and Lower Arm
Rol PD Controler
ol
DAC
OUTPUT SIGNALS TO VOICE COIL MOTOR CONTROLLERS
HALL EFFECT POSITION SENSOR SIGNALS
rst and elbow position
MU AC
..........
Vkist and
DS1 104MUJXADC
wrist1ontolsig l
S
DAC
-"P0fl
Ebow PID Controler
DS11I 4DACC4
elbow control sga
ENCODER
MASTER SETUP
A
DS1104DACC3
DS1 104ENCSETUP
Trjectory generator
Block diagram of PID controller for 4DOF arm
Figure 6.1
Where the block diagram for the individual PID controllers is:
WRIST PID CONTROLLER
PROPORTIONAL
CONTROL
WRIST
POSITION
I
SIGNAL
WRISTPGAIN
From
>risne
WRIST DESIRED
POSITION
CONTO
OUTPUT TO
Integrator
n2t
WRISTIGAIN
Saturation
ACITAO
DERIVATIVE
CONTROL
DWRIST VEl=LOCITY
SIGNAL
in2
WRISTDOAIN
Figure 6.2
Block diagram of wrist PID controller
45
The PID control law is as follows:
V = -Ki (O, -
,, ) - Kii (Oi - Ods,) - Kdo, ;
(8)
where V is the control input for joint i, ?ids is the desired angular position of joint i, and
K;i, and Kd, are the proportional, integral and derivative control system gains,
respectively.
Position and velocity information for the roll joints is obtained via magnetic encoders,
and position information for the bicep and wrist joints is obtained via linear Hall-effect
sensors. Consequently, the velocities of these joints are obtained by differentiating their
position signals. As expected, high frequency electrical noise make this signal difficult to
interpret, so low-pass filters with roll off frequencies of 100 rad/s were implemented on
each of the position signals to be differentiated.
Kp;,
6.3 PID CONTROL
WITH GAIN SCHEDULING
The next control system developed was a PID controller with a gain scheduling
algorithm that varies the controller gains as functions of joint angular positions. Without
developing a full system model, the gain scheduler adjusts the gains to compensate for
the dominant non-linearities in the physical system. The system parameters for which
gains were adapted were: position-dependant actuator constants, position-dependant
actuator attachment radius, and position-dependant gravitational torques.
The block diagram of the PID Controller with gain scheduling is shown in figure
6.3.
46
4 DEGREE OF FREEDOM PID CONTROLLER WITH GAIN SCHEDULING
PID CONTROLLER
OUTPUT SIGNALS TO DC (ROLL) MOTOR CONTROLLERS
ENCODER POSITIONNELOCITY SENSOR SIGNALS
n
DAC
oiionIforearm toll position
Ini
-- J
Eric delta position!N
DS1I
DS10DA
Outi
2
04ENCPOSC1
C1C
forearm roll control signal
forearm roll velocity
pper arm toll
positi n
In
upper arm toll velocity
Upper
L
DS 1
ut2
upper
arm roll control signal
DAC
und Lower Arm
DS1104DACC2
Rol PO Controller
OUTPUT SIGNALS TO VOICE COIL MOTOR CONTROLLERS
HALL EFFECT POSITION SENSOR SIGNALS
wrist coto
WX _ADC
twist and elbow position
DS1104MUXADC
V
DAC
inl)
DS10DA2C
tist and Elbow P Controller
IS1
DA _C
elbow contiol signa.1
DAC
DS11D4DAC_C3
GAIN SCHEDULER
NOMINAL P GAINS
ADJUSTED P GAINS
SCALING BLOCKS TO VARY GAINS FOR DYNAMIC EFFECTS
forearm roll
-tpp
tap
C_
wristP
uT
faP
biP'
0ut2
10biP'
wristP
Out3
elbo-P
ewristP
Ou4elbowP
Actuator attachment
Outl
-
0ut2
--
--
0ut3
-
-
0ut
--
--
-
Spring compensation
-
fap
biP
Outl
0 ut2
W ristp
Out3
0 ut
elbowP
Compensation for varying
actuator constant
radius
-
-
---
-
-
-
faP
Outi
biP
QUt2
twistP
OutV
upper
1
arm roll (bicep)
brPfinal
wrist voice coil
pt
elbowP' ___0 4
i
Gravity compensation
w
elbow voice cod
elbowPfinal
elbowP
Figure 6.3
Block diagram of 4DOF PID control system with gain scheduling
The control law for the PID controller with gain scheduling is:
V1 = -K
1
(O1 -ides)
K
f
(e - Oides) K
;
(9)
the same as the PID control law, except that in this case the proportional control gains,
Kpi, are position-dependant. The gains vary according to angular position of the joint, to
compensate for non-linear gravitational effects, a varying actuator constant, and the nonlinearity associated with the point of attachment of the VCA to the arm segment on which
it acts. The dynamic models of these effects are discussed in section 5.2; the exact
relationships between the proportional gains and the angular positions are described
below, for each of the 3 effects.
47
6.3.2
POSITION-DEPENDANTACTUA
TOR CONSTANTS
To counteract the position-dependant actuator constants of the VCAs, the
controller proportional gains vary according to:
Kpki
=
Kpinom *
K.
(1 -
m )+Kpmin ;
(10)
K,ma
where KpkI is the proportional control gain adjustment factor, Kpinom is the nominal
(starting) gain, to be adjusted by the gain scheduler, Kpmin is the minimum proportional
control gain, and Kmi and Kimax are actuator constants, as defined by equations (5) and (6).
6.3.3
GRAVITA TIONAL EFFECTS
Control gains were also adjusted to compensate for non-linear gravitational
effects. The effect of gravity on the second joint (the wrist joint) is negligible, since the
mass of this joint is very small. However, gravity plays a significant role on the torque
seen at the bicep joint. Consequently, the following gain-scheduling law was
implemented to vary the proportional control gain of the bicep VCA:
Kgi=Kino, *
Tgi
(11)
gi max
where Kpgi is the proportional control gain adjustment factor, Kpinom is the nominal
(starting) gain, to be adjusted by the gain scheduler, Tgi is the varying gravitational torque
(determined in equation (2)), and TgImax is the maximum gravitational torque experienced
at the joint.
48
6.3.4
VARYING RADIUS AT WHICH THE VCA ACTS ON ARM SEGMENT
Thirdly, the effective radius at which the actuator clevis acts on its arm segment
(and thus the torque delivered to that arm segment for a given force input) varies nonlinearly with angular position of the joint. The proportional control gains were therefore
varied for both the bicep and forearm VCAs according to the following gain-scheduling
law:
KP,, =
Kpinom
* (1-
R.
'
R a
)+Kpmj;
(12)
where Kpri is the proportional control gain adjustment factor, Kpinom is the nominal
(starting) gain, to be adjusted by the gain scheduler, Ri is the varying actuator radius of
attachment, Rimax is the maximum actuator radius of attachment, and Kpmin is the
minimum proportional control gain.
Ultimately, the control system proportional gain is adjusted according to:
Kp =Kki * Kpgi *Kpri
(13)
6.4 MODEL-BASED CONTROL SYSTEM WITH PD FEEDBACK
Finally, a controller for the wrist VCA was designed with a feedforward term
based on the dynamic model discussed in section 5.2, in addition to a simple PD feedback
term. The block diagram of the Model-based control system with PD Feedback is shown
in figure 6.4.
49
WRIST ACTUATOR CONTROLLER WITH DYNAMIC MODEL-BASED
FEEDFORWARD COMPENSATION AND PD FEEDBACK CONTROL
MODEL-BASED FEEDFORWARD CONTROLLER
THETADESIRE0
J
THETADOTESIRED
THETADOUBLEDOTDESIRED
POSI [O -EPE NAT
MOTOR CONS TANT
ELECTRICAL
DYNAMICS
(CALCULATION
DESIRED TRAJECTORY
GENERATION
R
RADIUS
RM SEGMENT
MOMENT OF INERTIA
OF ATTACHMENT
ACTUATOE
(U)
~0
1
CALCULATIONOF
SPRING FORCE
BASED
CRE
CEENTRL
TOGTAL
FEEDFORWARD
DAMPING COEFFICIENT
DESIRED
VO0LTAGE)
i2desitdV2desired
EL
CONTROL
DA
D
GAINTORQUE
(FEEEEFORWARD)
DYNAMC MODEL
ON
ACCELERATION DUE
TO GRAVITY
FEED BACK CONTROL
SIGNAL
MASS OF ARM SEGMENT
IGAIN
.030
DISTANCE TO CENTROID
WRIST SIGNAL
WRIST
POSITION
THETAWRIST
CALCULATION OF ELBOW POSITION1
WR/STAND ELBOW
ELBOW SIGNAL
POSITAO SENSOA
SOTGALS
I
CALCULATION OF ELBOW POSITION
TAETAG
ELBOW POSITION
TAELDOW
CALCULATION OF
THETA2
PD FEEDBACK CONTROLLER
PD
TE
WRISTPOSITION
CONTROLLER FEEDBACK CONTROL SIGNAL
WRIST PID CONTROLLER
(FEEDBACK)
Figure 6.4
Block diagram of model-based controller with PD feedback
The model-based control law is:
V, =V - KPW(o
-6Wd/)- K w , ;
(14)
Where V, is the calculated desired input voltage to the wrist actuator, from (2), (3), (5),
(6), and (7), based on desired angular position, velocity, and acceleration, and based on
estimates (and measured values) of each of the constant parameters in the dynamic
model. The second and third terms in the control law represent the PD (feedback) portion
of the controller. The controller uses the feedforward term, Y,, to provide best-estimate
control signals to track a prescribed trajectory in an open-loop fashion, and corrects for
imperfections in the model (via the proportional control term) by observing and
comparing actual joint positions (using feedback sensors) with desired positions, and
adjusting the control input accordingly. The third and final term in the control law
provides some damping to the system to minimize overshoot and smooth the motion of
the arm.
50
Table 6.1 shows each of the relevant estimated and measured parameters in the
dynamic model. Some of the constant parameters ( 1 ,2, for example) do not appear
explicitly in the dynamic equations, but are used in the derivations of some of the terms.
Table 6.1
ARM AND ACTUATOR DESIGN PARAMETERS RELEVANT TO WRIST CONTROL SYSTEM
DEVELOPMENT
Parameter Name
Description
L2
Re 2
Inductance of wrist actuator
Electrical resistance of wrist
actuator
Peak wrist actuator constant
Minimum wrist actuator
constant
K2max
K2min
02mid
1a2
0a2
M2
12
1e2
g
Estimated or Measured
Value
3.2 mH
3.7150
7.6 N/A
6.2 N/A
Half-stroke wrist angle
0.855 rads (490)
See figure 5.4
See figure 5.4
Mass of hand
Moment of inertia of hand
Distance from wrist axis to
centroid of hand
Acceleration due to gravity
0.0224 m
0.262 rads (15')
0.08 kg
3.75x10-5
0.03 m
9.8 m/s2
51
CHAPTER 7.
RESULTS
7.1 ACTUATOR RESULTS
Despite not being optimized for cost, force, or power density, the VCAs
developed show promising results as robotic actuators. Their simple design affords
cheap, fast construction. Their concentric form factor enabled smooth integration into the
robot arm, and minimized the number and size of bearings that were necessary. A light
lubricant was used on the actuator shafts, resulting in extremely low mechanical
Coulombic and viscous friction, and completely silent actuation. The actuators have high
bandwidths and are easy to control. They are backlash and cog-free, and their low
friction characteristics permit high control system gains. They have some inherent
damping due to back EMF, which, when used in conjunction with a damping term in the
control law, allows fluid, smooth, life-like motion.
7.1.1
PERFORMANCE
The VCAs performed according to specifications they were designed to meet.
The maximum 10-second peak pressure was approximately 50KPa, which is
approximately 1/7th that of human muscle. Significantly higher pressures are achievable
for shorter durations. Peak actuator constants are 16.2 N/Amp and 7.1 N/Amp for the
bicep and wrist actuators, respectively. The force performance curves are shown in
figure 7.1.
52
Actuator Performance
100
908070-
z
o
60
50
0
40
30
-Forearm
10-
-
Actuator
Bicep Actuator
0
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
Current (A)
Figure 7.1
Plot of forearm and bicep actuator force performance
As the figure shows, the actuator performance is roughly linear over a broad range of
currents (and temperatures) - a linearity that could be exploited to obtain information
regarding arm loading, or to use current measurements to implement basic force control
without the use of expensive and cumbersome force sensors. In an attempt to compare
VCAs with some of the other forms of actuation discussed in table 2.1, table 7.1 shows
some of the measured results of key actuator performance metrics for the VCAs. Some
metrics are only discussed qualitatively (noise level, for example), as absolute
measurements may be difficult to obtain or characterize.
53
Table 7.1
ACTUATOR PERFORMANCE RESULTS
Performance Metric
Value
Discussion
Peak Pressure
50 kPa
Peak Volumetric Power
Density
1.26 MW/m2
Peak Mass Power Density
300W/kg
Peak Volumetric Force
Density
470kN/m 3
Peak Mass Force Density
112N/kg
Maximum Strain
38%
Work Density
5.6J/kg
This value is conservative.
Destructive tests were not
conducted. This is
approximately 4-7 times
lower than human muscle.
Efficiency is speed
dependant - this value
assumes a total efficiency of
50%
Approximately 50% higher
than human muscle
Relatively low characteristic of
electromagnetic actuators
Relatively low due to the
high density of magnetic
materials used. A problem
that future research should
address
Strains up to 50% are easily
obtained, at the cost of
inefficiency due to heating
in the coils
High material density hurts
this value, but long
achievable strains help
offset the effects of the high
Speed
Fast
actuator mass
A conclusive test was not
conducted, but smooth
actuator response is
achievable well above 100
Hz.
Noise level
Silent
Bicep actuator mass
1.37kg
Wrist actuator mass
0.5kg
Silent at any speed - a
strong advantage of voice
coils
54
7.1.2
SHORTCOMINGS
As can be seen in chapter 6, a major shortcoming of the VCAs from the control
standpoint is their inherent non-linearity. Several properties of VCAs make them prone
to non-linear torque delivery, when used as robotic actuators. Many of these properties
have been exposed in this thesis, including position-dependant actuator constants, and the
sinusoidally-varying torque delivery that results from using a linear actuator to drive a
rotary joint. These non-linearities, however, can be modeled without much difficulty,
and control strategies can be very effective at overcoming them. Also, careful geometric
decisions can counteract some of the resultant deficiencies. For example, as the actuator
constant weakens significantly near the end of the range of motion of the VCA, springs
can be used with force characteristics that oppose this effect.
Clearly, the mass of the actuators is a concern, and an area for future development
as well. Research has been done in the areas of fluid cooling for electromagnetic
actuators, lightweight, high permeability magnetic materials, and increased air gap flux
density. Research such as this will push VCAs toward being lighter and stronger, and
therefore more competitive as robotic actuators.
7.2 ARMRESULTS
The arm is both an effective evaluation platform for the VCAs, as well as a
promising prototype of a dextrous, interactive arm for future robots in the Robotic Life
Group. The arm moves smoothly, quickly and quietly enough to communicate
effectively and convincingly. It has ample strength to perform useful tasks, such as
holding a tool or a part, opening a door, or lifting a light object. In addition, the arm has
the strength, agility, and quality of motion to execute complex tasks such as surface
tracing or catching and throwing, if an appropriately sophisticated control system is used.
7.2.1
INTERACTIVITY
Interactions with the arm are compliant and safe. The inherent backdriveability of
the actuators gives the arm an organic feel, despite its strength. As a result of the arm's
compliance, collisions with objects or people in its environment are not damaging to the
arm, its actuators, or the objects or people with which it is colliding. The silence and
speed of the actuators further enrich the interaction, making it more human-like.
7.2.2
STRENGTH
The Voice coil actuators have peak forces approximately 11 times greater than
their weights, making them very suitable for this robotic application. The design goals
discussed in table 3.1 were met, and end effector forces of 20 N were realized. This is
adequate strength for a robot of this size to effectively execute low-moderate force tasks
(shaking hands, pushing objects, holding and using various tools - screwdrivers, a drill,
55
or a hammer, for example). This strength also allows accelerations that permit the robot
to exhibit a range of emotions (shock, surprise, and excitement, for example) in
convincing and organic ways.
7.3 OVERALL SYSTEMRESULTS (WITH CONTROLLERS)
The implementation of different control systems on the arm and actuators further
highlighted the strengths and weaknesses of VCAs as robotic actuators, as well
evaluating the utility of this type of robotic arm in a robot intended for human interaction.
Since the actuators and the mechanical system were designed with fluid, silent, highbandwidth, backlash-free motion in mind, it is important that no other components in the
system compromise this performance. For relatively low control system gains, the motor
controllers behaved predictably and smoothly. The result is reasonable tracking
performance at low frequencies, using all types of control systems that were tested. At
higher frequencies, the simpler control systems (such as the basic PID controller)
preserved the smoothness of motion, despite poor trajectory tracking performance. The
model-based controller, however, exhibited excellent quality of motion and trajectory
tracking performance and a wide range of frequencies.
Control system gains were kept low for the evaluation of the arm for several
reasons. First, low-stiffness, heavily damped motion was desired to ensure safe
interaction, and smooth arm motion. Consequently, fast, stiff actuator responses were
sacrificed for an organic quality of motion. Secondly, the upper and lower arm roll
degrees of freedom are clearly the weak link in the arm design, meaning that at high
gains (or high accelerations) these actuators saturate. Keeping gains low permitted
smoother, more linear responses from these actuators. Thirdly, jitter problems in the
digital amplifier restricted the permissible control system gains. Beyond a certain gain
threshold, the response of the elbow actuator to externally applied loads was an erratic,
high frequency tremble. The high bandwidth of the VCAs make them sensitive to such
jitter in the control signal, despite filtering. Finally, characteristics of the components
used in the arm design imposed limits on permissible controller gains. Differentiated
noisy signals from the Hall-effect sensors at the elbow and wrist joints forced low
damping gains for these joints, and a structural resonance of the arm at approximately 36
rads/sec made high frequency, high stiffness trajectory control difficult. Such a structural
problem could be solved in the future by implementing compliance and dampening
elements at the shoulder.
7.3.1
RESULTS WiTH PID CONTROLLER
The trajectory tracking performance using the simple PID controller is shown in
figures 7.2 thru 7.5. The desired trajectories for each of the 4 degrees of freedom are
simultaneous sinusoids with frequencies of 9rads/s. Understandably, the 2 degrees of
freedom with the highest inertial loads have the worst tracking performance. The
56
tracking performance is reasonable at this, and lower frequencies, with maximum phase
lags of approximately 0.88 radians for the elbow and upper arm roll degrees of freedom.
Upper Arm Roll Position vs. Desired Upper Arm Roll Position, 9rads/sec (PID)
0.4-
+Actual
Upper Arm Roll Position
Upper Arm Rol Position
.Desired
0.3
0.2
0.1
-
0
-0.2
-0.3 -
.0
-0 A
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Upper arm roll tracking performance with PID control (9 rads/sec)
Figure 7.2
Forearm Rol Position vs. Desired Forearm Roll Position, 9rads/sec (PID)
0.6
*
-.
Actual Forearm Roll Position
Desired Forearm Roll Position
0.4
0.2
0
.~-0.2
-\-0.4-
-0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.3
Forearm roll tracking performance with PID control (9 rads/sec)
57
Elbow position vs. Desired Elbow Position, 9rads/sec (PID)
1 .4.
Actual Elbow Position
Desired Elbow Position
*
1.2
1
V
0.8
S
0.6
0~
Ob
0.4
0.2
0
-0.2 -
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.4
Plot of elbow tracking performance with PID control (9 rads/sec)
Wrist position vs. Desired wrist position, 9rads/sec (PID)
1.4
*
1.3
Actual Wrist Position
Desired Wrist Position
X
1.2
*
1.1
-
-
'90.9
*-
-0.8
0.7
0.6
-
-*
0.5
*
**
0. 4
0
0.1
0.2
0.3
0.4
0.5
0.6
+
0.7
0.8
1
0.9
Time (seconds)
Figure 7.5
Plot of wrist tracking performance with PID control (9 rads/sec)
58
7.3.2
RESULTS WITH PID CONTROLLER WITH GAIN SCHEDULING
The same trajectory tracking task was executed with the PID controller with gain
scheduling. While some marginal improvements were noticed over the PID controller,
the trajectory tracking performance was largely the same as that of the PID controller.
The most significant improvement is the decreased overshoot of the elbow actuator, as a
result of the modeling of the gravity-compensating springs at the elbow joint. The lack of
improvement of the gain scheduling controller over the PID controller implies that the
dominant effects affecting the controller performance are not the effects for which the
control gains were adjusted. Specifically, the inertial and damping effects play a major
role in the arm's response, as can be seen by the performance of the model-based
controller. The gain scheduler is affected very little by external forces acting on the arm.
The gains are bounded such that they remain within a stable range, regardless of the state
of the arm, or of the external load. The trajectory tracking results for the PID controller
with gain scheduling are shown in figures 7.6 thru 7.9.
Upper Arm Roll Position vs. Desired Upper Arm Roll Position, 9rads/sec (PID With Gain Scheduling)
0.4
Actual Upper Arm Roll Position
Desired Upper Arm Roll Position
0.3 -
02
-. 1
-0.2-
-0.3-
-0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.6
Plot of upper arm roll tracking performance with PID controller with gain scheduling (9
rads/sec)
59
Forearm Rol Position vs. Desired Forearm Roll Position, 9rads/sec (PID With Gain Scheduling)
0. 6.
iActual
Forearm Roll Position
Desired Forearm RoNl Position
0.41
0.2
0
-0.2
-0.4
-0.6 H
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.7
Plot of forearm roll tracking performance with PID controller with gain scheduling (9 rads/sec)
Elbow position vs. Desired Elbow Position, 9rads/sec (PID With Gain Scheduling)
*
Actual Elbow Position
Desired Elbow Position
0.8
0.6
t 0.4
0.2
0
-0.2L
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.8
Plot of elbow tracking performance with PID controller with gain scheduling (9 rads/sec)
60
1.4
Wrist position vs. Desired wrist position, 9rads/sec (PID With Gain Scheduling)
*
1.3
Actual Wrist Position
Desired Wrist Position
1.3-*
'0.79
0.6-
0.5-
0.40
+
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time (seconds)
Figure 7.9
7.3.3
Plot of wrist tracking performance with PID controller with gain scheduling (9 rads/sec)
R ESUL TS WITH MODEL-BAsED FEEDFoRWARD CONTROLLER WITH PD FEEDBACK
The armn exhibited excellent tracking performance with the model-based
controller. A sinusoidal trajectory tracking task with a frequency of 40rads/sec was
implemented first with the feedback controller alone, then with the feedforward term
added. The results of these two tests are shown in figures 7.10 and 7.11. Under feedback
control only, the response is diminished by almost 50%, and the joint position lags the
desired position by 90'. With the feedforward controller, the tracking performance is
extremely tight. The joint position lags the desired position by less than 10', and the
amplitude of the position is within I% of the desired amplitude. Clearly the dynamic
model (especially the representation of the arm's inertia) offers a great advantage over
the simpler control systems.
Despite the arm's excellent trajectory tracking performance with the model-based
controller, this controller is limited in its relevance for tactile interaction with the arm.
Unless the external force (in our case, most often a human) is included in the system
model, the controller can do nothing other than rely on the feedback portion of the
controller to maintain appropriate pressure. Once contact is established, the model has
little effect in helping the system respond to the external disturbance. The lack of
feedforward compensation, however, did not cause stability problems, as the feedback
gains remain constant, and the feedforward control inputs are bounded due to the inertia,
mass, and desired trajectories being bounded.
61
Wrist position vs. Desired wrist position, 40 rads/sec (Feedback Control Only)
1.4
*
-
Actual Wrist Position
Desired Wrist Position
1.3
-1NI
1.2
r-
0.9
0.8
0.7
0
0.05
Figure 7.10
0.1
0.15
0.2
0.25
0.3
Time (seconds)
0.35
0.4
0.45
0.5
Wrist actuator tracking performance with PD control, 40 rads/sec
Wrist position vs. Desired wrist position, 40 rads/sec (Feedback and Feedforward Control)
*
Actual Wrist Position
Desired Wrist Position
1.3
1.2
J
-
-
ca.
75
I
1
20.9
-
0.8
I
0.7
0.6'
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (seconds)
Figure 7.11
Plot of wrist actuator tracking performance with feedforward and feedback control, 40 rads/sec
62
Secondly, the step response performance of the model-based controller was compared to
that of the simple feedback controller. It can be seen from figures 7.12 and 7.13 that,
while the step responses of the two controllers are similar (due to very low control gains),
the steady state position error is significantly reduced by the model-based controller, due
to the gravity compensation in the dynamic model.
Wrist position vs. Desired wrist position, Step Response (Feedback Control Only)
*
Actual Wrist Position
Desired Wrist Position
1.1
1.05
I
0.95
8 0.90.85
0.u
-19_1
Mr
-
0.75
0.7
0.65
-0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.12
Plot of wrist actuator step response with simple PD control
63
Wrist position vs. Desired wrist position, Step Response (Feedforward and Feedback Control)
.
1 15
A1 Actual Wrist Position
Desired Wrist Positin
1.05-
0.95-
0.85
-
0.8-
0.750.7
0.65
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (seconds)
Figure 7.13
Plot of wrist step response with feedback and feedforward control
Finally, a test was performed to determine at what frequency the model-based controller
became ineffective. Figure 7.14 shows the results of an 80rads/sec sinusoidal tracking
task, in which the performance of the model-based controller is greatly diminished. The
model-based controller gave tracking performance within 20' of phase lag and 10%
amplitude matching at frequencies up to 55 rads/sec.
64
Wrist position vs. Desired wrist position, 80 rads/s (Feedback and Feedforward Control)
1.4
'
Actual Wrist Position
Desired Wrist Position
1.3
1.2
-
a
-5
1.1
11
III
-
-
0.9
0.8
0.7
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (seconds)
Figure 7.14
Plot of wrist actuator tracking performance with feedforward and feedback control, 80 rads/sec
65
CHAPTER 8.
FUTURE WORK AND CONCLUSION
8.1 FUTURE WORK
This research has demonstrated the viability of VCAs as robotic actuators, and
has highlighted their major deficiencies. These deficiencies include: high actuator mass,
low actuator pressure, non-linearities that complicate control, and inefficiency at low
speeds. Two major veins of future work would greatly benefit the development of VCAs
as robotic actuators.
First, research into the design and materials used in VCAs would help resolve
some of the fundamental problems with VCAs mentioned above. Novel, lowimpedance mechanical transducers could be developed to address the problem of low
actuator pressures. Further to that cause, research in the area of low resistivity coil
materials or improved heat dissipation would help to increase actuator pressures by
allowing more current to flow in the coils, potentially without a decrease in efficiency.
Most importantly, materials with higher magnetic remanences, higher heat tolerances,
and lower densities would greatly reduce the mass of VCAs, while increasing actuator
performance.
Secondly, development of sophisticated control systems designed specifically for
VCAs will enrich the interaction between humans and robots, and enable more useful
tasks to be accomplished. Such tasks (grasping an object or shaking hands with a person,
for example) depend heavily on control system design. For convincing tactile
interactions, force, impedance, or hybrid control [16] will be necessary to fully take
advantage of the VCAs' excellent quality of motion. In the near future, a 4DOF forcesensing hand will be mounted on the arm for experimentation with end-effector force
control.
In an attempt to tackle the low pressure problem associated with VCAs, we have
conducted preliminary research on compact electro-hydraulic systems that marry the high
power densities of electromagnetic actuators with the high pressures of hydraulic
actuators. We believe that a strong potential exists in using a voice coil-driven miniature
hydraulic pump, packaged within a hydraulic actuator (cylinder) to leverage some of the
benefits of the two forms of actuation. Such an actuator could eliminate the need for
hydraulic lines and valves, while taking advantage of the strong, fluid motion of
hydraulic systems, the form factor of the two forms of actuation, their quiet and
controllable operation, and their high power densities. Fig. 8.1 shows our prototype of a
self-contained electro-hydraulic actuator comprising a brushless DC motor, a miniature
gear pump, and bellows-style pistons at either end. The system is fully sealed, and the
motor operates submerged in the working fluid. Initial results have revealed that VCApiston pump designs may afford higher pressures and efficiencies.
66
P gure
8.1
Photo ot sealed, self-contained electro-hydraulic actuator
8.2 CONCLUSiON
The advantages and compromises in using VCAs as actuators for HRI robots is evident.
They have been chosen for their high quality of motion, fast response, controllability, and
form factor. The tradeoff is that they are less efficient at low speeds than other actuation
technologies, and must be oversized due to their low pressures. This preliminary study
has shown that, for applications to medium DOF, non-mobile robots for tactile interaction
with people, this tradeoff is acceptable.
67
BIBLIOGRAPHY
[1]
J. Hollerbach, I. Hunter & J. Ballantyne "A comparative analysis of actuator technologies for
robotics", 0. Khatib, J. Craig & Lozano-Perez Eds, The Robotics Review 2, MIT Press, Cambridge
MA 1992, pp. 299-342.
[2]
J. Madden, N. Vandesteeg, P. Anquetil, P. Madden, A. Takshi, R. Pytel, S. Lafontaine, P. Wieringa,
and I. Hunter, "Artificial Muscle Technology: Physical Principles and Naval Prospects", under review,
submitted to The Journalof Oceanic Engineering,2004.
[3] Y.Bar-Cohen, Ed, "Electroactive Polymer (EAP) Actuators as Artificial Muscles, Reality, Potential,
and Challenges", SPIE Press, 2001.
[4] S.E. Salcudean and L. Stocco, "Isotropy and Actuator Optimization in Haptic Interface Design", IEEE
International Conference on Robotics & Automation (San Fransisco, CA) April, 2000.
[5] Anthony C. Morcos, "Voice Coil Actuators for use in Motion Control Systems", online content
available at: http://www.motion.org/9804morc.htm, 1998.
[6] H. Asada and J-J. Slotine, "Robot Analysis and Control", Wiley Interscience, 1986.
[7] Y. Bar-Cohen, Online content available at: http:/ndeaa.jpl.nasa.gov/nasa-nde/lonnas/cap/EAP-
web.htm, 2004.
[8] E.J. McCormick, "Human Factors in Engineering and Design", McGraw-Hill, 1976.
[9] Online content available at: http://ndeaa.jpl.nasa. -ov/nasa-nde/lonmmas/cap/actuators-comp.pdf, 2004.
[10] K. Youcef-Toumi, "Deisgn and Control of Direct-Drive Robots - a Survey", 0. Khatib, J. Craig &
Lozano Perez Eds, The Robotics Review 1, The MIT Press, 1989, pp. 2 83-302.
[11] N. Hogan and E. Colgate, "Stability Problems in Contact Tasks", 0. Khatib, J. Craig & Lozano Perez
Eds, The Robotics Review 1, The MIT Press, 1989, pp. 3 3 9 -3 4 8 .
[12] J.Paine, "Piezoelectric Step and Repeat Hydraulic Motor Phase I STTR", online content available at:
http://www.darpa.mil/dsothrust/natdev/chap/briefinLs/timchap2000davl /Paine PiezoStep.pdf, 1999.
[13] Online content available at: http://www.consult-g2.com/papers/paper I 5/paper.html.
[14] Honda Motor Company, Online content available at: http://world.honda.coi/ASIMO/P3i/spec/, 2004.
[15] Gill Pratt, "Biologically Inspired Components of Robots - Sensors, Actuators and Power Supplies",
unpublished, 2002.
[16] J.J. E. Slotine, W. Li, "Applied Nonlinear Control", Prentice-Hall, 1986.
68